I had a quick look on google and within 0.19 seconds 9 of the first 10 links publicly reveal how to crack the root password, and your story sounds genuine enough. This technique cannot be used to hack into systems on the internet because you need physical access to the keyboard and CD drive anyway.
1a) Some versions of unix allow you to boot single user without needing the root password, so the first technique would be to add "single" or "1" to the linux boot options list for your unix partition.
When booted single user you might need to mount the root filesystem read/write, so find out what it is by looking at /etc/fstab or /etc/vfstab, then
mount -o remount,rw /dev/hd1a /
replacing /dev/hd1a with whatever your boot device is
1b) If single user still needs a password, then boot from a rescue disk or knoppix
You'll need to identify the root filesystem, so take a look at the output from
fdsik -l
Then mount the root filesystem
mount -t reiserfs /dev/hda1 /mnt
2) Next you just edit out the password from the /etc/shadow file (or /mnt/etc/shadow if you mounted root on /mnt), or on some ditributions the password is in /etc/passwd.
Example before
root:x3FrTg6uYT7.:0:0:root:/:/bin/sh
and afterwards
root::0:0:root:/:/bin/sh
3) Finally after rebooting the system, if you still get prompted for a password just hit ENTER.
NB: There can be further complications if you are using software mirroring.
E.g. for Veritas Volume Manager mirroring on Solaris take a look at Sun Microsystem's SRDB 11828 (which I wrote when I worked there)